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Biochemistry I
Problem Set 3
September 6, 2016
Due Tuesday September 20, 2016
This problem set should take you ~90 min to complete.
1. (6 pts, 15 min) You are growing a 0.5 L culture of bacteria in growth media that is buffered with 0.05 M
phosphate, at an initial pH = 6.2. After 6 hours of growth, the pH rises to 6.5 due to the release of organic
bases by the bacteria. Since the bacteria grow optimally at pH 6.2 you would like to return the pH back to
6.2. Calculate how many moles of HCl would you need to add to the 0.5 L culture to restore the pH to 6.2.
You can assume that the second pKa value for phosphate is 7.2. [Hint: Sketch a titration curve to
approximate how many equivalents of acid you would need to move from a pH of 6.5 to 6.2. Alternatively,
sketch a curve of fraction protonated versus pH to help you calculate the number of equivalents that would
be required to move the pH from 6.5 back to 6.2].
2. (8 pts, 10 min)
i) Estimate the pI of the peptide that you viewed for problem 5 on Pset 2 (sequence is Ala-Glu-Leu). You can
do this by calculating the charge at a number of different pH values, or use excel to do these calculations
for you (5 pts)
ii) Assume you want to purify this peptide for a mixture of other peptides. One method is ion exchange
chromatography, where small beads with a surface charge are used to capture charged molecules from
solution by electrostatic forces between the bead and the charged molecule. In this case you have anion
exchange beads which have a positive charge (so anions stick). What should the pH of your solution be to
capture your peptide? How would you release your peptide from the bead after washing away other
peptides that did not bind to the bead? (3 pts).
3. (8 pts, 15 min) Digestion of a peptide with Trypsin, Chymotrypsin, and Cyanogen bromide produced the
sequence data given below. Note that it was only possible to perform Edman degradation for seven cycles,
i.e. it is only possible to determine the sequence of the first seven residues of any peptide. Keep in mind
that the peptide may have been longer. Determine the sequence of the original peptide. Show how you
arrived at the sequence and demonstrate that your final answer is consistent with the experimental data.
i. The products from Cyanogen bromide treatment gave peptides with the following sequences:
Arg-Ser-Cys-Met Gly-Arg-Ser-Thr-Gly Trp-Gly-Ala-Val-Ile-Leu-Met
ii. Trypsin digestion produced one free amino acid (not identified), and the following peptide
sequences:
Ser-Thr-Gly
Ser-Cys-Met-Trp-Gly-Ala-Val
iii. Chymotrypsin digestion produced the sequences of the following peptides:
Arg-Ser-Cys-Met-Trp
Gly-Ala-Val-Ile-Leu-Met-Gly
4. (5 pts, 5 min) A famous scientist has determined the structure of an important
new protein by a technique called X-ray crystallography. They proudly show
you the Ramachandran plot for their new protein structure (on right). On the
basis of the Ramachandran plot, why is unlikely that they have determined the
structure correctly? Please justify your answer.
Use the Jmol page to answer the following questions.
5. (5 pts, 10 min) Pick the first (closest to the amino terminus) -stand in your
protein and give the following:
i) Starting residue (ns)
ii) Ending residue (ne)
iii) Length (l), in Å, of the beta strand (measured from the same atom in the
start and ending residue), then calculate the length of a single residue in a beta strand = l/(ne-ns+1)
Can’t find the amino terminus? Try the following using the menu: Color:Structures:Cartoon:By
scheme:Group. The amino terminus will be blue. See the Jmol tutorial for how to measure distances.
6. (5 pts, 10 min) Complete the same analysis as Q5, but for the α-helix in the protein.
i) What is the relative distance spanned by a single residue in an alpha helix versus a beta strand?
ii) What is the linear distance spanned by one turn of a helix?
7. (5 pts, 10 min) Use this helix (from Q6) to determine the rule, or relationship, that describes the relative
position in the polypeptide chain of mainchain hydrogen bond acceptors and donors in an -helix, i.e. if you
are given the residue number of an acceptor (e.g. residue # 15), your rule should predict the residue
number of the hydrogen bond donor (Sample incorrect answer: The hydrogen bond donor for a residue in a
helix is found at i+1, i.e. the residue immediately following donates the hydrogen bond.
8. (5 pts, 10 min) The absorbance (A) of a solution of your protein was measured at =280 nm and found to be
1.5. The path length is 1cm. What is the concentration of the protein in this solution? Please show your
work. Instructions on determining the composition of a protein are given on the Jmol page.